ibeta Model Robeco's quantitative credit market timing model WHITE PAPER July 2014 For professional investors

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1 WHITE PAPER July 2014 For professional investors ibeta Model Robeco's quantitative credit market timing model Patrick Houweling Paul Beekhuizen Georgi Kyosev Jeroen van Zundert ibeta Model 1

2 TABLE OF CONTENTS 1. Introduction Model Description Performance Conclusions References ibeta Model 2

3 1. Introduction Investors in credit markets have several ways to generate outperformance. The two main ways are issuer selection and market timing. In this paper we focus on the market timing decision, i.e. predicting whether the credit market return will be positive or negative in the investment period and adjusting the portfolio beta accordingly. Specifically, we discuss Robeco s quantitative credit market timing strategy. This strategy is used as the performance driver in the Robeco Quant High Yield Fund, which was launched in March Direction and Size of Positions The quantitative market timing strategy consists of two components: the direction of the position, generated by the ibeta model, and the size of the position, based on the Robeco Credit Risk Model. Together they determine whether a long or a short position will be taken and how large that position will be. This white paper focuses on the ibeta model; in an earlier white paper we described the Robeco Credit Risk Model. 1 Variables The ibeta model combines various variables that each have a clear economic rationale and academic foundation. The variables use information from different markets and have different lookback periods. For example, the model uses information not only from the credit market, but also from the equity market and the equity option market. And it combines long-term, multi-year trends with short-term trends measured over several months. This way a diversified and balanced model score is calculated that provides a forecast of the direction of the credit market. Strong Performance in Research and Live Period The ibeta model was developed in 2010, as a spin-off of an existing model whose history can be traced back to The research used data from June 2004 (the inception date of the CDS indices) until April The back-test performance of the ibeta model over this period was strong, with information ratios around In the subsequent four years, we monitored the performance of the model by weekly generating forecasts and evaluating the strategy return. The performance was very satisfactory in this live period, with information ratios between 0.9 and 1.0. Since March 2014 the High Yield signals of the model are used in the Robeco Quant High Yield Fund. This white paper provides a detailed description of Robeco s ibeta model. In Section 2 we describe the variables of the model, including their economic rationale. Further, we detail how we determine the model direction and how we calculate the position size. In Section 3 we show the model s performance, both in the research period and in the live period. Section 4 concludes. 1 See Smart credit investing: Risk Points and their applications by Beekhuizen & Houweling (2013). ibeta Model 3

4 2. Model Description The ibeta model generates weekly return forecasts for the main credit markets. These markets and the accompaning CDS indices are listed in Table 1. Note that in the Robeco Quant High Yield Fund only the High Yield signals and CDS indices are used. Please refer to the Markit (2014) documentation for more information on CDS indices. Table 1. Credit markets in the ibeta universe and their CDS indices Market CDS index full name CDS index short name US Investment Grade CDX Investment Grade CDX IG US High Yield CDX High Yield CDX HY European Investment Grade itraxx Main itraxx Main European High Yield itraxx CrossOver itraxx XO Source: Markit In this section we provide a brief history of the ibeta model. We describe the variables and how they are combined to calculate the direction of the market timing strategy. We also show how we integrate the risk forecasts of the Robeco Credit Risk Model to calculate the position size. We conclude by showing the tool that is used in the weekly update process. 2.1 A Brief History Robeco has a long tradition in developing market timing models. The model for predicting government bond returns was developed in 1994 and the equity market timing model in The history of the ibeta model can be traced back to That first predecessor of the model aimed at predicting corporate bond market returns and already contained three of the current four themes: Equity, Short-Term Trend and Seasonal. In the course of the years the model was enhanced several times. Model enhancements included adding new variables to increase diversification within the model, refining variable definitions to reduce measurement noise and integrating risk forecasts to stabilize the risk profile over time. In 2007 we introduced the fourth theme to the model, Long-Term Trend. The current version of the model was created in At that time the model was fine-tuned to the application to credit default swap (CDS) indices, whereas the original model was developed using bond indices. This entailed increasing the data frequency of the model from monthly to weekly to capture the faster dynamics of CDS versus bonds. Since May 2010, the model has remained unchanged. 2.2 Variables The ibeta model constructs its return forecast for a credit market using multiple variables. These variables have been selected after extensive empirical research, which demonstrated a convincing relationship between the variables and credit market returns. Moreover, our own research is backed by academic research, either on credit markets, or on equity markets. For all variables a clear economic interpretation exists, based on the insights from the behavioral finance literature. We believe that human behavior, such as herding and over- and under-reaction, leads to systematic market mispricings that can be exploited with a disciplined investment process. The model variables can be grouped into ibeta Model 4

5 credit spread (bps) MSCI (total return index) four themes: Equity, Short-Term Trend, Long-Term Trend and Seasonal. The themes exhibit low mutual correlations, with each theme capturing a separate economic effect. Equity Information about a company s well-being is reflected in different markets, including the equity market and the credit market. These markets are theoretically linked via the Merton (1974) structural credit risk model. In this model a firm s equity is seen as a call option on its assets, and a corporate bond as a default-free bond plus a written put option. This implies that positive news about the firm s assets results in positive equity returns and positive bond returns, establishing a positive relation between the equity market and the credit market. However, an increase in volatility is positive for equity holders, but negative for debt holders, implying a negative relationship between volatility changes and credit returns. These patterns have been confirmed in empirical studies as well, both for corporate bonds and for credit default swaps; 2 see Figure 1 and Figure 2 for an illustration. The ibeta model uses equity returns and changes in equity volatility to predict credit returns. Both variables are examples of information spill-over from the equity market to the credit market. The academic literature explains such spill-over patterns by the slow diffusion of information from one market to another; see Hong et al. (2007). Figure 1. European High Yield credit spreads (itraxx XO, left axis) vs. European equity market total return index (MSCI EU, right axis) 0 7, , ,000 1,200 1,400 1, ,000 4,000 3,000 2,000 itraxx XO (LHS) MSCI EU (RHS) Sources: Barclays, Bloomberg 2 Equity-credit relationship: see e.g. Keim and Stambaugh (1986), Fung et al. (2008), Ehlers et al. (2010), Hong et al. (2012) and Haesen and Houweling (2013). Equity volatility- credit relationship: see e.g. Figuerola-Ferretti and Paraskevopoulos (2012) and Haesen and Houweling (2013). ibeta Model 5

6 credut spread (bps) VIX (%) Figure 2. US Investment Grade credit spreads (CDX IG, left axis) vs. US implied equity volatility (VIX, right axis) CDX IG (LHS) VIX (RHS) Sources: Barclays, Bloomberg Short-Term Trend In financial markets there is abundant evidence of trending markets. This may be explained by herding behavior, i.e. market participants following each other, or investors underreaction to new information. For credit markets trend behavior has also been documented. 3 Moreover, trend information from one credit market may spill-over to other credit markets, e.g. from the United States to Europe, or from Investment Grade to High Yield. Our trend variables are designed to capture and exploit these patterns. The ibeta model defines trends using moving average rules; see e.g. Faber (2007, 2013). Such a rule compares the average credit spread calculated over a recent period with the average over a longer period; whenever the two averages cross, this changes the direction of the trend variable; see Figure 3 for an illustration. Moreover, the ibeta model acknowledges that trends may change faster when the credit market is more volatile. Therefore, in a volatile environment, the moving average rules in the model look back on a shorter period of time, so that they react faster to changes in the market direction. 3 Herding behavior: see e.g. Barberis and Shleifer (2003). Underreaction: see e.g. Daniel et al. (1998). Trends in credit markets: see e.g. Clinebell et al. (1996), Hong et al. (2012) and Haesen and Houweling (2013). ibeta Model 6

7 credit spread (bps) credit spread (bps) Figure 3. High Yield credit spreads with fast and slow moving averages Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec bullish signal bearish signal credit spread fast moving average slower moving average Sources: Barclays, Robeco Long-Term Trend Asset class returns are related to variations in the business cycle; see e.g. Fama and French (1989). In contrast to short-term trends, which last several weeks or months, these long-term patterns describe multi-year cycles. Years of economic growth are associated with positive equity and corporate bond risk premia and a negative bond risk premium, while periods of economic downturn are associated with opposite return patterns. Van Vliet and Blitz (2011) found that economic regimes capture time-variation in risk and return of asset classes and used regimes to define a strategic asset allocation strategy. One of the regime indicators in their study is the credit spread. The ibeta model uses long-term trends in credit spreads to capture business cycle variations in a way that is most directly related to the credit market. Below-average credit spreads are associated with a benign economic environment and positive credit market returns, and vice versa for aboveaverage credit spreads; see Figure 4 for an illustration. Moreover, an exit rule is applied to prevent losses due to strong market reversals that typically occur at the end of a cycle. Figure 4. High Yield credit spreads with long-term moving average bullish signal bearish signal Barclays US High Yield Index long term average Sources: Barclays, Robeco ibeta Model 7

8 Seasonal The academic literature documents various seasonal effects in asset classes. Although there is no single economic rationale of these effects, one possible behavioral finance explanation is the optimism cycle ; see. e.g. Doeswijk (2008). Towards the end of the year, investors start to look forward to the new year, often with overly optimistic expectations. This results in attractive returns for risky assets during the last part of the year and during the beginning of the new year. For equity markets, this seasonal pattern is often summarized as: sell in May and go away, but remember to come back in November; see e.g. Bouman and Jacobsen (2002). Haesen and Houweling (2013) documented that this pattern also exists in credit markets. Kamstra et al. (2014) found the opposite seasonal effect for government bonds. The Seasonal variable in the ibeta model implements this pattern by generating a positive signal in the winter months (November- April), and a negative signal in the summer months (May-October). Figure 5 shows that the average returns are indeed lower in the summer than in the winter for each of the four major CDS indices. Since the nature of this variable is different from other variables in the model (binary vs. continuous), we adjust the calculation of the Seasonal signal to make sure that it has the same impact on the model score as the other variables. Figure 5. Annualized returns for US Investment Grade (CDX IG), European Investment Grade (itraxx Main), US High Yield (CDX HY) and European High Yield (itraxx XO) credit default swap indices, over the period June 2004 May 2014 in summer months (May October) and winter months (November April) 10% 9% 8% 7% 6% 5% 4% 3% 2% 1% 0% CDX IG itraxx Main CDX HY itraxx XO Summer Winter Sources: Barclays, Robeco 2.3 Determining the Direction of the Position To determine the forecast direction for each credit market, we first combine variable scores into a theme score and then combine theme scores into a model score. We use standardized scores to account for differences in scale and volatility between the variables. Furthermore, we use equal weights within and between themes. The rationale behind the equal-weighting scheme is that it is very hard a priori to identify which variable will work best in the next period. Therefore, an equally weighted model provides the best diversification, just like in an investment portfolio. Robeco research shows that this is a conservative and robust approach that gives more stable results than more complex rules. ibeta Model 8

9 Next, the US and European scores are combined into a global score, both for Investment Grade and High Yield. Our research shows that regional allocation does not add value using the current set of model variables. Finally, the model score is translated into a model forecast using an implementation rule that strikes a balance between benefiting from the model s forecasts and reducing turnover. The implementation rule can be loosely described as: change the direction only if the model score passes a threshold convincingly, otherwise keep the current direction. More formally, the model direction is long (bullish view on credit market returns) if the model score is above 0.2, but is only changed to a neutral view if the model score drops below 0.1. The zone between 0.1 and 0.2 is used to prevent unnecessary turnover. The same holds for model scores between 0.2 and 0.1; see Figure 6 for an illustration. Figure 6. Implementation rule to translate model score into model direction 0.3 long 0.2 unchanged neutral unchanged short Source: Robeco 2.4 Determining the Size of the Position Previous Robeco research showed that the volatility of credit markets is strongly timevarying; see Houweling et al. (2007). This implies that if we were to implement the direction of the ibeta model with a static position size, the volatility of the strategy would show strong time variation too. By using the risk forecast of the Robeco Credit Risk Model to determine the position size, we can substantially reduce the time variation in the strategy s volatility. In short this means that we scale down the position if the credit market is more volatile, and vice versa; see Beekhuizen and Houweling (2013) for more details on the risk model and its application to beta positioning. Figure 7 shows that this method of dynamically determining the position size based on expected market volatility substantially reduces the strategy volatility in volatile market circumstances, most notably in and Hence, integrating the risk model forecasts in the strategy makes the risk profile more stable over time. ibeta Model 9

10 volatility (%) Figure 7. 1-Year rolling window volatility of ibeta strategy applied to global High Yield (CDX HY & itraxx XO) with static and dynamic position sizes 8% 7% 6% 5% 4% 3% 2% 1% 0% static position size dynamic position size with integrated risk management Sources: Barclays, Robeco Another decision in the implementation is the weight of the various CDS indices in the portfolio. Because we do not have a view on the individual index constituents, we choose to construct the portfolio in such a way that it is equally exposed to each of the constituents. For instance, the Robeco Quant High Yield Fund takes positions in the CDX High Yield index, with 100 constituents, and the itraxx CrossOver index, which has 60 constituents. 4 To get equal exposure to each of the 160 constituents, the instrument weights are 100/160=62.5% and 60/160=37.5%. 5 Similarly, in Investment Grade the number of constituents is 100 for US (CDX Investment Grade) and 125 for Europe (itraxx Main), resulting in weights of 100/225=44.4% and 125/225=55.6%. 2.5 Weekly Model Updates Every week the ibeta model is updated using a tailor-made tool. This tool provides an overview of the model signal, the model score, the theme scores and the position size. Implementation of the model signal takes place in Robeco s Fixed Income department. Figure 8 displays a screen shot of the update tool. 4 The constituents in CDX High Yield and itraxx CrossOver are mutually exclusive. 5 The number of constituents in itraxx CrossOver will increase to 75 in September Then, the US weight in the Robeco Quant High Yield Fund will become 100/175=57.1%, and the weight of Europe 75/175=42.9%. ibeta Model 10

11 Figure 8. Screen shot of the ibeta update tool Source: Robeco ibeta Model 11

12 3. Performance In this section we describe the performance of the ibeta strategy. We start with a description of the performance in the research period and in the live period. Then we motivate how much return we expect in the future. 3.1 Strong Performance in Research and Live Periods The investment strategy combines the return forecasts of the ibeta model with the position sizes that are calculated using the Robeco Credit Risk Model. Table 2 shows the back-test performance of the strategy from June 2004 until May The starting date of June 2004 coincides with the inception date of the itraxx and CDX instruments. Note that the ibeta model was spun off from an existing model that was developed on Barclays corporate bond indices for which historical data is available since The performance of the model themes on these long-term data is described in our academic paper; see Haesen and Houweling (2013). Table 2 reports performance for two sub-periods: the research period until May 2010 and the live period afterwards. For Investment Grade we use a target volatility of 1% and for High Yield of 3%; in both cases this corresponds to about 1/3 of the market volatility. By appropriately scaling the position sizes, the strategy can also be used with smaller or larger target volatility levels. The table shows that the ibeta strategy performed well in both the research period and the live period. For Investment Grade the information ratios are about 0.8, while for High Yield they are about 0.9. It is reassuring to see that the strategy continued to perform well after the research period. 6 Table 2. Annualized return, volatility and information ratio for the ibeta strategy applied to global Investment Grade (CDX IG & itraxx Main) and global High Yield (CDX HY & itraxx XO) over the research period (June April 2010), live period (May 2010 May 2014) and total period (June 2004 May 2014) Global Investment Grade Mean Volatility Information ratio Research period Jun04-Apr % 0.93% 0.75 Live period May10-May % 0.86% 0.89 Total period Jun04-May % 0.90% 0.81 Global High Yield Research period Jun04-Apr % 2.78% 0.93 Live period May10-May % 3.22% 0.99 Total period Jun04-May % 2.97% 0.95 Source: Robeco Figure 9 and Figure 10 display the cumulative strategy returns for Investment Grade and High Yield, respectively. The period from 2004 to 2014 includes various periods of market 6 The value of your investments may fluctuate. Returns obtained in the past are no guarantee for the future. ibeta Model 12

13 stress (most importantly the 2008 subprime crisis and the European sovereign debt crisis), but also periods of strongly positive market returns (e.g. in 2009 following the subprime crisis) and tranquil periods (like ). On average, the ibeta strategy has been able to generate positive returns in most of these market circumstances. By looking at the chart more carefully, we can also observe several weaker periods around market reversals: mid-2005 (after unrest in the market following the Ford and General Motors downgrades to High Yield), second half of 2007 (after the start of the subprime crisis) and several short-lived drawdowns in (positive or negative events around European sovereigns). Figure 9. Cumulative return of the ibeta strategy applied to global Investment Grade (CDX IG & itraxx Main) over the period June 2004 May 2014; the vertical line indicates the end of the research period 8% 6% 4% 2% 0% Source: Robeco Figure 10. Cumulative return of the ibeta strategy applied to global High Yield (CDX HY & itraxx XO) over the period June 2004 May The vertical line indicates the end of the research period 35% 30% 25% 20% 15% 10% 5% 0% -5% Source: Robeco ibeta Model 13

14 Figure 11 and Figure 12 display returns of the ibeta strategy over calendar years, for Investment Grade and High Yield, respectively. We observe that the Investment Grade strategy was negative in only 1 out 11 years, while the High Yield application generated negative returns in only 2 out of 11 years. Figure 11 Calendar year returns of the ibeta strategy applied to global Investment Grade (CDX IG & itraxx Main) over the period June 2004 May * 2004 is not a full year, but June December. ** 2014 is not a full year either, but January May. Returns in partial years are not annualized. 3.0% 2.5% 2.0% 1.5% 1.0% 0.5% 0.0% -0.5% 2004* ** Source: Robeco Figure 12 Calendar year returns of the ibeta strategy applied to global High Yield (CDX HY & itraxx XO) over the period June 2004 May * 2004 is not a full year, but June December. ** 2014 is not a full year either, but January May. Returns in partial years are not annualized 7.0% 6.0% 5.0% 4.0% 3.0% 2.0% 1.0% 0.0% -1.0% -2.0% -3.0% Source: Robeco 2004* ** ibeta Model 14

15 3.2 Expected Future Performance At Robeco Quantitative Research we aim to conduct research as prudently as possible. We do this by using behavioral finance as a theoretical framework, using inputs from academic literature, and by proper out-of-sample testing. Our experience shows that as a rule of thumb the expected real-life performance of a quantitative strategy is about half of the back-tested performance. Still, we strongly believe in model persistence, backed by behavioral finance insights that human behavior will persist in the future and can therefore be exploited in a disciplined, rules-based investment process. Above we showed an information ratio of about 0.8 to 1.0 for the ibeta strategy. Applying the rule of thumb, we expect an information ratio of 0.4 to 0.5 going forward. For the volatility we target the same levels as in the back-test period, so about 1% for Investment Grade and 3% for High Yield. These numbers imply a future performance of about 0.5% per annum for the Investment Grade strategy and 1.5% per annum for the High Yield strategy. ibeta Model 15

16 4. Conclusions Robeco s ibeta model is a quantitative credit market timing model fine-tuned to credit default swap indices. The history of the model goes back to 2000, when the first version of the model was developed to forecast corporate bond market returns. The ibeta model provides weekly return forecasts based on multiple factors that each have a clear economic intuition and academic foundation. The factors include equity market returns, changes in equity market volatility, short-term and long-term trends in credit markets and seasonal patterns. The model contains various enhancements to smartly predict credit market returns, such as the adaptive speed of the short-term trend factor, the exit rule for the long-term trend factor and the usage of cross-market trends. The market direction forecasts of the ibeta model are combined with risk forecasts of the Robeco Credit Risk Model to calculate position sizes. In this way the volatility of the strategy return is relatively stable over time. The strategy realized strong performance, both in the research period until April 2010, and in the live period from May 2010 onwards. In both periods information ratios of were achieved for Investment Grade and High Yield credit markets. Given the usual decay of model performance in reallife we believe an information ratio of 0.5 is a more realistic expectation for the future. Since March 2014 the ibeta model is used in the Robeco Quant High Yield Fund. This fund offers exposure to the global High Yield market by investing in highly liquid CDS indices. The fund uses the ibeta model as performance driver. The fund s high liquidity makes it suitable for investors who want to invest in High Yield for a possibly shorter investment horizon. The quantitative alpha driver of the fund is attractive for investors who are looking for diversification in management styles. See our publication Quant investing in liquid High Yield (April 2014) for more details on the Robeco Quant High Yield Fund. Patrick Houweling, PhD Paul Beekhuizen, PhD Georgi Kyosev Jeroen van Zundert Quantitative Researcher Quantitative Researcher Quantitative Researcher Quantitative Researcher & Portfolio Manager ibeta Model 16

17 5. References Barberis, N., Shleifer, A., 2003, Style investing, Journal of Financial Economics 68(2), Beekhuizen, P., Houweling, P., 2013, Smart credit investing: Risk Points and their applications, Robeco white paper. Bouman, S., Jacobsen, B., 2002, The Halloween indicator, 'Sell in May and go away': Another puzzle, American Economic Review 92(5), Clinebell, J.M., Kahl, D.K., Stevens, J.L., 1996, Time series estimation of the bond default risk premium, The Quarterly Review of Economics and Finance 36(4), Daniel, K.D., Hirshfleifer, D., Subrahmanyam, A., 1998, Investor psychology and security market under- and overreactions, Journal of Finance 53(6), Doeswijk, R.Q., 2008, The optimism cycle: Sell in May, De Economist 156(2), Ehlers, S., Gürtler, M., Olboeter, S., 2010, Financial crises and information transfer: An empirical analysis of the lead-lag relationship between equity and CDS itraxx indices, working paper, Faber, M.T., 2007, A quantitative approach to tactical asset allocation, Journal of Wealth Management 9(4), Faber, M.T., 2013, A quantitative approach to tactical asset allocation: Update, working paper, Fama, E.F., French, K.R., 1989, Business conditions and expected returns on stocks and bonds, Journal of Financial Economics 25(1), Figuerola-Ferretti, I., Paraskevopoulos, I., 2012, Pairing market and credit risk, working paper, Fung, H.G., Sierra, G.E., Yau, J., Zhang, G., 2008, Are the U.S. stock market and credit default swap market related? Evidence from the CDX indices, The Journal of Alternative Investments 11(1), Haesen, D., Houweling, P., 2013, On the nature and predictability of corporate bond index returns, working paper, Hong, Y., Lin, H., Wu, C., 2012, Are corporate bond market returns predictable? Journal of Banking and Finance 36(8), Hong, H., Touros, W., Valkanov, R., 2007, Do industries lead stock markets?, Journal of Financial Economics 83(2), Hong, Y., Lin, H., Wu, C., 2012, Are corporate bond market returns predictable?, Journal of Banking and Finance 36(8), Houweling, P., Penninga, O., van Leeuwen, E., Ben Dor, A., Hyman, J., Dynkin, L., 2007, Duration Times Spread: A new measure of spread exposure in credit portfolios, The Journal of Portfolio Management, Kamstra, M.J., Kramer, L.A., Levi, M.D., 2014, Seasonal variation in Treasury returns, working paper, ibeta Model 17

18 Keim, D.B., Stambaugh, R.F., 1986, Predicting returns in the stock and bond markets, Journal of Financial Economics 17(2), Markit, 2014, Markit credit indices: A primer, Merton, R.C., 1974, On the pricing of corporate debt: The risk structure of interest rates, The Journal of Finance 29(2), van Vliet, P., Blitz, D.C., 2011, Dynamic strategic asset allocation: Risk and return across the business cycle, The Journal of Asset Management 12, ibeta Model 18

19 Important information Robeco Institutional Asset Management B.V. (trade register number: ), hereafter Robeco, has a license as manager of UCITS and AIF's of the Netherlands Authority for the Financial Markets in Amsterdam. It is intended to provide the professional investor with general information on Robeco s specific capabilities, but does not constitute a recommendation or an advice to buy or sell certain securities or investment products. All rights relating to the information in this presentation are and will remain the property of Robeco. No part of this presentation may be reproduced, saved in an automated data file or published in any form or by any means, either electronically, mechanically, by photocopy, recording or in any other way, without Robeco's prior written permission. The information contained in this publication is not intended for users from other countries, such as US citizens and residents, where the offering of foreign financial services is not permitted, or where Robeco's services are not available. The prospectus and the Key Investor Information Document for the Robeco Funds can all be obtained free of charge at ibeta Model 19